Theory and Application of Computation in Statistical Physics

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

The broad theme of this award is to understand complex systems in statistical physics using a combination of computational and theoretical tools. The research has three related components: the random field Ising model; the development of new algorithms; and, the analysis of physical systems from the standpoint of computational complexity. Informed by new hypotheses and recent results, the phase transition of the random field Ising model will be studied using a replica exchange, i.e., parallel tempering, algorithm, a push-relabel algorithm, to find ground states, and real-space renormalization group techniques. The objective is to understand the nature of phase transition and particularly the singularities in the specific heat. Phase transitions in long-ranged correlated pore spaces, e.g., aerogels, will be considered. This work will potentially answer some long-standing theoretical questions concerning phase transitions in the presence of quenched disorder. The random field Ising model is believed to describe the phase transitions in fluids absorbed in porous materials and the results of this research should impact chemical physics and chemical engineering. In order to advance computational studies of spin systems, research is planned on the development and analysis of algorithms with an emphasis on replica exchange and cluster methods. Replica exchange methods are among the most powerful tools available for studying complex systems with competing interactions. Developing this class of algorithms has an importance that goes beyond the present study and may be relevant to problems ranging from protein folding to combinatorial optimization. In addition to providing algorithmic support for the random field Ising model study, one goal of this research is to develop cluster algorithms for dynamical problems. The third topic is a study of the parallel computational complexity of simulating systems in statistical physics. Efficient parallel algorithms will be constructed and analyzed for various systems including diffusion limited aggregation and growing networks. Based on insights gained from examining various models, general results will be sought relating structural properties and parallel computational complexity. For example, it is conjectured that, under relatively unrestrictive conditions, the absence of long-range correlations implies the existence of a fast parallel sampling algorithm. Investigations at the interface of theoretical computer science and statistical physics have the potential for yielding profound insights in both fields. Computational complexity provides a robust, formal way to measure history dependence in statistical physics and will sharpen our understanding of how and why physically complex systems sometimes emerge from simple rules and randomness. Besides the usual broader impacts associated with the research, this project will involve undergraduate physics students in computer simulations, especially in the third topical area. %%% The broad theme of this award is to understand complex systems in statistical physics using a combination of computational and theoretical tools. The research has three related components: the random field Ising model; the development of new algorithms; and, the analysis of physical systems from the standpoint of computational complexity. What is particularly interesting about this research program is that the work is at the interface between statistical physics and theoretical computer science. There have been a number of recent examples where statistical physics has contributed to computer science. This research will continue to focus on this fertile interface. Students working on these projects will be well positioned to contribute to both condensed matter physics and computational science. ***